A note on N-soliton solutions for the viscid incompressible Navier-Stokes differential equation

Abstract

Repetitive curling of the incompressible viscid Navier-Stokes differential equation leads to a higher-order diffusion equation. Substituting this equation into the Navier-Stokes differential equation transposes the latter into the Korteweg-de Vries-Burgers equation with the Weierstrass p-function as the soliton solution. However, a higher-order derivative of the studied variable produces the so-called N-soliton solution, which is comparable to the N-soliton solution of the Kadomtsev-Petviashvili equation.

35 pages (including cover letter & QA-section), 22 Figures, article,3 Tables

References in corpus (3)

• The Discrete Nonlinear Schrödinger equation - 20 Years on
• The Static Elliptic $N$-soliton Solutions of the KdV Equation
• On self-similar solutions of the vortex filament equation

Cited by in corpus (1)

• Exact Distributions for the Solutions of the Compressible Viscous Navier Stokes Differential Equations: An Application in the Aeronautical Industry